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More music theory anyone?

Let's talk about the "rules" of music. Music is the child of art and mathematics. We of course have the artistic qualities from mother art, in that the same 7 notes (and their variations) can be written into millions of combinations, each. But, father math has provided us a ridgid structure in which all music spawns.

In these, we're going to group the rules into two large categories:Static Rules Which are rules that hold true no matter what we do to the rule.
AndChanging Rules These are the rules that change, based on what us as humans can manipulate it into.

*We'll define "breaking" a rule as creating a new rule that will always hold true, as will the parent rule. We'll define "bending" a rule as creating a situation in which the original holds true, but the new rule only holds true under certain circumstances which come about as a direct result of our intervention and ONLY holds true when we force it to.

With static rules, when we break the rule, we have created a NEW rule that will be just as static as the rule before. The changing rules are a bit more tricky, as they adapt to what we do, and we adapt them to what we want.

Let's have a couple changing rules first. The general rule of composing and orchestration is that we have tubas play the tuba part and violins play the violin part. But that is thrown out the window when we arrange the same part for a different instruments. We bend the rule, but we don't "break" it. We merely "bend" the rule and we arrange something for say all horns like this. Although we consider the arrangement the intellectual property of the arranger, he hasn't really created anything new. It's still the same melody, only played by all Vienna horns. This "rule" however, only holds true when we force it to, and we play it as such. The original arrangement of the piece is still considered the original piece, and the arrangement is exactly that...just parts rearranged.

Another one of these changing rules is that we compose double bass parts...in the double bass range. This however we manipulate by playing several octaves abouve. But again we haven't really created anything new. We're either playing the double bass part outside of the truly "effective" range of the instrument, or playing the part in the effective range of another instrument on the bass.

So enough of that, because there are an infinite number of examples that we can think of that would fit that rule. Let's look at the static rules. (Reminder: this are rules that break and we create a new rule and both are new or original).

The best example of this are the scales. All scales are variations of a majour scale. In steps, it's a classic teaching tool to mark a majour scale like this:
W W H W W W H
1 2 3 4 5 6 7
This pattern holds true with every majour scale:
Cmaj:
C D E F G A B
WWHWWWH

Bbmaj:
Bb C D Eb F G A Bb
WWHWWWH

And so forth and so on. This can be proven on a piano keyboard:
From C to D is one WHOLE step.
From D to E is one WHOLE step.
From E to F is one HALF step.
From F to G is one WHOLE step.
From G to A is one WHOLE step.
From A to B is one WHOLE step.
And finally from B to C is one HALF step.
That's Cmaj. Does the same hold true for say...C#maj? Let's find out. We're going to follow our pattern.
From C# one whole step is: D# (or Eb).
So far we have:
C# D# what's next?
One whole step from D# up is F.
C# D# F.
One HALF step up from F is of course F#.
C# D# F F# (or Gb).
One whole step up from F# is G#.
C# D# F F# G#
The next whole step up from G# is A#.
C# D# F F# G# A#.
One more whole step and we're almost there! One more whole step from A# (or Bb) is C.
C# D# F F# G# A# C.
The last step is the half step that brings us back to C#.
C# D# F F# G# A# C C# which is the C#maj scale.

We've proven that the pattern of WWHWWWH steps proves true to always produce a majour scale. No matter what we do, we create a majour scale. But let's change this rule a bit though. Our new rule is that for every majour scale we're going to flatten our 3rd. So now the pattern looks like WHWWWWH. We've created a new rule to define a scale. Let's take this and apply it to Cmaj so that it produces this:
C D Eb F G A B C. This is actually a new and separate scale mode called the melodic minour scale. By dong this, we break the original rule, and create a new mode, while the original is still preserved. Infact, you can switch just about anything within the scale you like, to get a new mode.

Let's talk about one last example of a static rule. This one, is a little different and is considered a physical limitation, not so much a rule. And that is that there is a certain point that we as humans cannot reproduce what is on paper. Such as this:
This of course is theoretically possible but physically impossible. For one, it is out of the effective range of the instrument. For two, the human embouchure cannot switch between those extremes in that time frame.

Enjoy

Last edited by musicteach; Jan-16-2013 at 11:33.

Music education opens doors that help children pass from school into the world around them-a world of work, culture, intellectual activity, and human involvement. The future of our Nation depends on providing our children with a complete education that includes music. -Gerald Ford

Thanks! A lot of people see music theory and go "Arg...theory...why do I need this technical mumbo jumbo?" and are afraid of it. I try to break it down in more manageable chunks. These are...by the way...the same concepts, examples, and basically the same text I use with my theory students.

Music education opens doors that help children pass from school into the world around them-a world of work, culture, intellectual activity, and human involvement. The future of our Nation depends on providing our children with a complete education that includes music. -Gerald Ford